Electronics Laboratory, Department of Physics, University of Patras, Patras 26500, Greece

1. A novel symbolization scheme for multichannel recordingswith emphasis on phase information and its applicationto differentiate EEG activity from different mental tasks Stavros I. Dimitriadis,Nikolaos A. Laskaris, Vasso Tsirka, Sofia Erimaki, Michael Vourkas, Sifis Micheloyannis, Spiros Fotopoulos Electronics Laboratory, Department of Physics, University of Patras, Patras 26500, Greece Artificial Intelligence & Information Analysis Laboratory, Department of Informatics, Aristotle University, Thessaloniki, Greece Medical Division (Laboratory L.Widιn), University of Crete, 71409 Iraklion/Crete, Greece Technical High School of Crete, Estavromenos, Iraklion, Crete, Greece Phasedynamics Φ [a b b c d e a b … ] http://users.auth.gr/~stdimitr

2. Outline Introduction -Multichannels EEG recordings -math calculations (control, comparison and multiplication) -multifrequency approach (from θ to γ) -symbolic dynamics in a multichannel fashion Methodology -Neural gas for symbolization -Different signal presentations (filtered signals, instantaneous amplitude and phase) -Network representation of neural-gas based symbolic dynamics -Compute directed GE (global efficiency) - Compare GE between the three possible pairs of conditions

3. Outline Outline of the Methodology Results Discussion

4. Symbolic dynamics is a powerful tool for studying complex dynamical systems Many techniques of this kind have been proposed as a means to analyze brain dynamics but most of them are restricted to single-sensor measurements Analyzing the dynamics in a channel-wise fashion is an invalid approach for multisite encephalographic recordings, since it ignores any pattern of coordinated activity that might emerge from the coherent activation of distinct brain areas.

5. Motivation We suggest, here, the use of neural-gas algorithm (Martinez et al. in IEEE Trans Neural Netw 4:558–569, 1993) for encoding brain activity spatiotemporal dynamics in the form of a symbolic timeseries. We intended to introduce the first multichannel approach for symbolization brain dynamics. Multichannel symbolization can unfold the “true” complexity of brain functionality !!

6. Outline of our methodology

7. Data acquisition: Math Experiment 18 subjects 30 EEG electrodes Horizontal and Vertical EOG Trial duration: 3 x 8 seconds Single trial analysis 3 Conditions: Control Comparison Multiplication The recording was terminated when at least an EEG-trace without visible artifacts had been recorded for each condition

8. Filtering Using a zero-phase band-pass filter (3rd order Butterworth filter), signals were extracted within six different narrow bands ( from 4 to 45 Hz) Artifact Correction Working individually for each subband and using EEGLAB (Delorme & Makeig,2004), artifact reduction was performed using ICA -Components related to eye movementwere identified based on their scalp topography which includedfrontal sites and their temporal course which followed the EOGsignals. -Components reflecting cardiac activity were recognizedfrom the regular rythmic pattern in their time course widespreadin the corresponding ICA component.

9. Neural-Gas algorithm Neural-Gas algorithm providesinput space representations by constructing data summaries ( via prototypical vectors). Its agradient descent procedure imitating gas dynamics within data space to calculate the prototypes.

10. Neural-gas based symbolization Transform a multichannel dataset into a symbolic sequence A codebook of k code vectors is designed by applying the neural-gas algorithm1 to the data matrix The reconstructed version of is denoted as To compute the fidelity of the overall encoding procedure,an index which is the total distortion error divided by the total dispersion of the data is adopted: In the present study,we considered as acceptable encoding the one produced with the smallest k and simultaneously satisfied the condition that should be less than 8%.

11. & estimation We first estimated the observed probability (a, b) that symbol a is followed by symbol b within the symbolic timeseries s(t). To detect the significantly correlated appearance of symbols, we need to estimate the probability of random co-occurrence of these two symbols. We denote as p(a) and p(b) the probabilities of finding the two symbols in s(t). The symbol a can occupy positions ranging fromthe first to the (T - 1)th position,where T is the length of s(t). For each fixed position i of a, with i = 1, …, (T - 1), there are (T – 1 - i) possible positions for b to appear in the sequence. Hence, the number of possible transitions a -> b within s(t) is given by the equation:

12. Transform to Computing for all the pairs of k symbols, we construct a co-occurence matrix CM. To transform to , we first sum the values of each raw of the CM and then we divide each element of the raw with the sum. As a result, the sum of each raw of the new matrix will be equal to 1 and will now tabulated values. A weight can be associated with the link from a to b, based on the extent to which the number of observed transitions deviates from the expected value

13. Building the codebook network Establishing links between each pair of symbols 0.9 0.6 The process is repeated for every pair of symbols, creating a codebook network with possible misconnections that correspond to forbidden patterns

14. Computing the GE of the codebook network Its values range between 0 and 1, with high values indicating an increased (with respect to randomness) number of state transitions, and hence a highly non-stable system (Latora and Marchiori 2001).

15. Different signal representations Apart from the frequency range, we tested extensively if the (filtered) signal in its original form, or in a form that either emphasizes amplitude or phase dynamics, facilitates better the differentiation between different recording conditions. We applied the Hilbert transform (Cohen 1995), which returns the instantaneous amplitude A(t) and instantaneous phase φ(t) and is defined as follows:

16. Differentiation of task-related brain dynamics The new symbolization scheme, followed by the codebooknetworkanalysis, was applied, in a contrastive fashion, forall possible pairs of recording conditions (control—comparison,control—multiplication and comparison—multiplication). For every frequency band and each of the threedifferent signal representations (i.e. x(t), A(t), u(t)), thepair of GE-measures was derived independently for each subject. To summarize across subjects, the computed set ofGE-pairs were analyzed via the Wilcoxon-test (P < 0.001). The statistical analysis of GE-values showed that phaserepresentation was the most suitable one for detecting taskrelatedchanges in brain dynamics.

17. Global efficiency (GE)averaged values correspondingto the three possiblecomparisons

18. Conclusions A symbolization scheme capable of handling multichannelrecordings of brain activity and useful for contrastingdynamics from different conditions was introduced andapplied to EEG data from mental calculations. Among the outcomes of this study was that duringmultiplication GE values are higher than during comparison(for all frequency bands). Consideringthe emerging patterns of coordinated activity as animportant aspect of underlying mechanisms, we developeda symbolic dynamics methodology that respects brain’smultistable character. Moreover, our approach shares the ‘prototyping’step with the pioneer work of segmenting brainactivity into functional microstates (Pascual-Marqui et al.1995). Our scheme can be readily adapted to various recordingmodalities (MEG, Fmri etc.) and used for comparingdynamics between healthy and diseased brains and basedon a variety of different representations (e.g. Networkmetrics time series; Dimitriadis et al. 2010a).

19. References [1]Dimitriadis SI, Laskaris NA, Tsirka V, Vourkas M, Micheloyannis S (2010a) Tracking brain dynamics via time-dependent network analysis. J Neurosci Methods 193:145–155 [2]Latora V, Marchiori M (2001) Efficient behaviour of small-world networks. Phys Rev Lett 87:198701 [3]Martinez T, Berkovich S, Schulten K (1993) Neural-gas network for vector quantization and its application to time-series prediction. IEEE Trans Neural Netw 4:558–569 [4]Pascual-Marqui RD, Michel CM, Lehmann D (1995) Segmentation of brain electrical activity into microstates: model estimation and validation. IEEE Trans Biomed Eng 42:658–665